[From moderator: Resent with apologies to those who received an empty message body...] Walter Tholen's recent message reminded me of a conjecture. Perhaps we have been too shy about stating our conjectures because, even among mathematicians, they may have seemed too technical. I seem to remember Peter Freyd saying once that the problem in category theory of proving sets were small (to find adjoints to functors for example) was analogous to finding numerical bounds in mathematical analysis. Surely by now, there are as many people who understand what a sheaf is as understand what the Riemann Hypothesis asserts (for example, local to global versus analytic continuation). So here is a problem I came up with in the 1970s. As with Fermat's Last Theorem, I don't particularly remember having any application for it. However, similar solved problems were used by Rosebrugh-Wood to characterize the category of sets in terms of adjoint strings involving the Yoneda embedding. By locally small I mean having homs in a chosen category Set of small sets. Problem. Suppose A is a locally small site whose category E of Set- valued sheaves is also locally small. Is E a topos? == Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]